The division between the "classical" and "quantum" worlds is most obvious when performing measurements. In classical systems, measurements generally are minimally invasive: you can find your height or weight, for example, without changing either quantity in a noticeable way. Quantum systems, however, have an interdependence between the instrument and the object being measured. In recent years, weak measurements have probed the division between the classical and quantum regimes by limiting the interaction between the apparatus and the system being measured.

Another approach to probing this distinction involves strong measurements that have no classical counterpart. Richard E. George and colleagues demonstrated incompatibility of the naive classical view in measurements on a modified diamond. As they described in a new PNAS paper, the equivalent classical system is similar to the old con known as the shell game: three shells, with a pea under one of them. Here, the act of "measuring" the pea's location has no effect on the system. But the researchers' quantum system excludes this classical behavior well beyond reasonable doubt or random chance.

We commonly speak and write of "measurement" in quantum systems, but it's important to remember that the measurement or apparatus need not be controlled by a human. In most cases we care about, experimentalists play an active role in measurement, including the study in this story. However, sometimes the environment—itself a quantum system—acts as a measuring device, effectively acting in the stead of an experiment. Despite the language we sometimes use, human involvement isn't the important factor in the outcome of a quantum interaction.

The shell game analogy

In the classic shell game con, a pea is placed under one of three shells on top of a table. The person running the game then moves the shells around in such a way as to confuse the player, who must bet where the pea now sits.

The quantum shell game in the current study works a little differently. In this case, the pea is placed randomly, and there are two players, whom we will name Alice and Bob (because that's just what we do). The "measurement" each can perform is a private peek under one shell at a time; the outcome of the experiment is either a "yes" or "no," depending on whether the shell contains the pea or not.

To complicate things, each of them can only look under two shells. Bob can look only under the leftmost and center shell. Alice can only look under the rightmost shell, but she can swap two of the shells and then peek again. However, Alice doesn't know which shell Bob looks under, so she can't swap shells to make sure he messes up. The two wager over the result of Bob's "measurement"—if Alice guesses the outcome of Bob's peek under the shell, then she wins. Alice can also "pass" on a round if she can't decide which way to bet.

That may be complicated, but the statistics are clear: from a classical standpoint, Alice can't win more than 50 percent of the time, even with her ability to skip a round of wagering. This is because Bob can choose which shell to "measure." However, from a quantum standpoint, Alice could conceivably win every bet. So, if they play the game enough times, the two players will know whether they're playing with a classical or a quantum system—between a game Bob can win half the time and a game he can never win.

The quantum shell game

The "pea" in the experiment in question was the spin of an electron on a single nitrogen atom, substituted for a carbon atom in a diamond. This is known as a "nitrogen vacancy," or NV, diamond. (Nitrogen has one more electron than carbon, resulting in a single controllable spin, which can be used for a variety of applications.) The spin can take one of three possible orientations, playing the role of the shells in the analogy.

Bob's role was played by microwaves, which stimulated the spin to transition, but only if it was in a particular configuration. If the result of the microwave stimulation was emission of light, that was equivalent to Bob finding the pea. If no photons came out, Bob failed to find the pea.

The equivalent to Alice's measurement was a simple determination of whether the spin was in one particular configuration out of the three. Unlike in the classical case, measuring the spin alters the quantum state of the system, since it affects the outcome of every subsequent experiment. The rules of quantum states ensured her a positive measurement (the pea under the rightmost shell) about 15 percent of the time, whatever the result of Bob's measurement—in stark contrast to the classical case. By passing on the "wager" in every round where her measurement turned up negative, she could win 67 percent or more in rounds where she placed her bet.

The final test involved Bob not performing any measurements. The outcome of the Alice measurement was unaffected by Bob's participation in the game, which is not a scenario allowed in the classical interpretation of the shell game.

Of course, Alice and Bob are fictional, and any macroscopic shell game would obey the rules of classical probability—including the key participation by Bob. However, the "shell game" using nitrogen vacancy diamonds agreed with the quantum predictions under 3,600 separate trials. Since "Alice" could not even detect if "Bob" measured the system or not, it showed that the difference between the classical and quantum perspective could not merely be explained away by measurement effects.

20 Reader Comments

For some reason, this article seems to be skipping more detail than usual for the quantum articles. I even had a hard time figuring out how the game works for the classical case. For the quantum case I'm totally lost as to where any of the results come from. (And I can usually follow the quantum articles on Ars pretty well.)

For some reason, this article seems to be skipping more detail than usual for the quantum articles. I even had a hard time figuring out how the game works for the classical case. For the quantum case I'm totally lost as to where any of the results come from. (And I can usually follow the quantum articles on Ars pretty well.)

I have to agree with you on that one. Somehow, even if the analogy is a good one, it wasn't clear enough for me.

In the classic shell game con, a pea is placed under one of three shells on top of a table. The person running the game then moves the shells around in such a way as to confuse the player, who must bet where the pea now sits.

No, that's the classic shell game.

In the classic shell game con, the person running the game uses slight of hand to make you think they've placed a pea under one of three shells, then moves the shells around as if trying to confuse the player in order to reinforce the premise that the pea is under one, then again uses slight of hand to place the pea that they were actually palming the whole time under one of the shells you did not pick.

That's what makes it a con, which is short for "confidence": getting you to trust that the rules of the game are being followed when in reality they are not.

So presumably in the quantum shell game con, there would similarly be a 'cheat' where you only think you have a 2/3rd chance of winning but in reality are going to lose every time. I dunno, maybe the street hustler is palming a qubit or something.

And, of course, the classic way to _beat_ the classic con is for the player to argue (in front of a very large and angry [but logically trained] crowd) that, once he points towards the candidate shell, he should not lift it, but rather he should lift the other two shells to prove that the pea lies under neither of them, and that, logically, the pea _must_ therefore be under the candidate shell. A shooting or a lynching is the logical conclusion.

For some reason, this article seems to be skipping more detail than usual for the quantum articles. I even had a hard time figuring out how the game works for the classical case. For the quantum case I'm totally lost as to where any of the results come from. (And I can usually follow the quantum articles on Ars pretty well.)

And, of course, the classic way to _beat_ the classic con is for the player to argue (in front of a very large and angry [but logically trained] crowd) that, once he points towards the candidate shell, he should not lift it, but rather he should lift the other two shells to prove that the pea lies under neither of them, and that, logically, the pea _must_ therefore be under the candidate shell. A shooting or a lynching is the logical conclusion.

The whole point of the con is that he's going to put the pea under one of the two shells that wasn't picked. So he'll pick up the other two shells, the pea will be under one of them logically demonstrating that the pea is not under the candidate shell, the player will lose their money, and your "logically trained" crowd failed to notice anything amiss and actually came away falsely believing that this game was on the up-and-up.

And it's exceedingly hard to pick up on the sleight-of-hand going on if the con man is skilled at it. Penn & Teller demonstrated the shell game using clear plastic cups and you still never noticed them actually putting the ball under the cup.

How would Bob ever know whether he was in a Classical game or a Quantum game? Every win would be more evidence for a Quantum game, but no win would rule out a Classical game. He could never be sure (but then we aren't ever going to be able to be sure about the theory of Quantum mechanics given that it is a scientific theory and can never be proven for certain).

How would Bob ever know whether he was in a Classical game or a Quantum game? Every win would be more evidence for a Quantum game, but no win would rule out a Classical game. He could never be sure (but then we aren't ever going to be able to be sure about the theory of Quantum mechanics given that it is a scientific theory and can never be proven for certain).

Well yes. So, eventually he'd "know" he was in a quantum game the same way we "know" we're in a quantum universe: The statistical distribution of outcomes matches the quantum prediction with such precision and would be so ridiculously unlikely to occur in the classical case that it would just be foolishly stubborn not to provisionally accept the quantum model.

Of course he'd probably be sure enough to change how he bets long before that.

The game's description is missing fundamental details. Do Alice and Bob take turns peeking? If so, who goes first? If not, what does happen?

Without that information the clarity of the quantum description doesn't matter.

Please clarify/rewrite the article.

There's definitely something wrong with this description. Even ignoring issues with who goes first or whether they take turns, Alice can win every round in the classical setting. Presumably she gets her peek before she makes her bet, and if she finds the pea she bets that Bob won't find it, because both of his shells are empty. If she doesn't find the pea, she passes. So she wins whenever she bets, with no quantum involvement required.

The game's description is missing fundamental details. Do Alice and Bob take turns peeking? If so, who goes first? If not, what does happen?

Without that information the clarity of the quantum description doesn't matter.

Please clarify/rewrite the article.

There's definitely something wrong with this description. Even ignoring issues with who goes first or whether they take turns, Alice can win every round in the classical setting. Presumably she gets her peek before she makes her bet, and if she finds the pea she bets that Bob won't find it, because both of his shells are empty. If she doesn't find the pea, she passes. So she wins whenever she bets, with no quantum involvement required.

Similarly, the "swap" ability would seem to kick up her percentage over the base 50/50, without even factoring in the "pass" option - she's got knowledge of 2/3 of the shells.

The game's description is missing fundamental details. Do Alice and Bob take turns peeking? If so, who goes first? If not, what does happen?

Without that information the clarity of the quantum description doesn't matter.

Please clarify/rewrite the article.

There's definitely something wrong with this description. Even ignoring issues with who goes first or whether they take turns, Alice can win every round in the classical setting. Presumably she gets her peek before she makes her bet, and if she finds the pea she bets that Bob won't find it, because both of his shells are empty. If she doesn't find the pea, she passes. So she wins whenever she bets, with no quantum involvement required.

And that is, i think, the whole point. To test if the behavior is by classic probability rules or quantum rules.

If anyone tries to explain quantum physics to you with an analogy. Stop them, they are wrong. (Ironically they are likely trying to explain it like that because the physics is so detached from anything we traditionally observe, but thats exactly why its doomed to fail.)

The analogy breaks down nearly instantly when you realise that Alice cant keep track of whats going on. Thats why she cant just check and bet on a success every time after Bob has his go. She can still obtain success the vast majority of times but its through manipulating the probabilities, not directly controlling where the 'ball' is. (Its still probabilities in the classic just with different results.)

The whole game analogy is wholly confusing on every level and does nothing to help understand pretty much any component of the set up. (Which is a set of interrelated probability calculations that should allow Alice to build up enough information to guess correctly but for quantum reasons do not.)

Ive read some pretty heady papers before and managed to wrangle an understanding but this one seemed tailor made to confuse. (I had thought it was a poor summary but seriously, read the paper, they take this game idea and run with it even as its falling apart around the maths.)

If anyone tries to explain quantum physics to you with an analogy. Stop them, they are wrong.

Not necessarily. Analogies can be very useful for explaining certain aspects of quantum mechanics. You just have to understand their limitations and not over-extend them. An analogy can't match every aspect of the thing being analogized -- if it did, then it wouldn't be an analogy.

For example, it's possible to explain how quantum entanglement doesn't allow FTL information transfer using a simple analogy of a red and black marble and two bags. You randomly put one marble in each bag, and then send them to two remote locations. When someone at one of the locations opens the bag and sees a red marble, they instantly "know" that the other person will find a black marble in theirs. However this doesn't actually allow them to learn anything faster than light. They knew the whole time that the contents of one bag would correlate with the other.

"Hold on!" you might say (or rather, people have said when I used this analogy). "Those marbles represent local hidden variables, which experimental violation of Bell's Inequality shows cannot explain quantum behavior!"

To which I say "Correct, but so what?" For the purpose of this analogy, that detail doesn't matter. We're not trying to recreate the statistical distribution of outcomes of a quantum entanglement experiment with marbles and bags. We're trying to explain in layman's terms how having two correlated outcomes separated by a great distance doesn't violate relativity, as long as the correlation is the result of events that occurred at or below c.

That's not defending the shell game analogy or its use in the paper, btw. The whole point is knowing when to stop. Over-extending an analogy to try to explain the things it isn't suited for is a recipe for disaster.